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We calculate the cross section for the $\gamma \gamma \to J/\psi J/\psi$process. Two mechanisms are considered: box (two-loop) diagrams of the order of$O(\alpha_{em}^2 \alpha_s^2)$ and two-gluon exchange of the order of$O(\alpha_{em}^2 \alpha_s^4)$. The first mechanism is calculated in theheavy-quark non-relativistic approximation while the second case we alsoinclude the effects of quantum motion of quarks in the bound state. The boxcontribution dominates at energies close to the threshold ($W <$ 15 GeV) whilethe two-gluon mechanism takes over at $W >$ 15 GeV. Including the bound-statewave function effects for the two-gluon exchange mechanism gives a crosssection 0.1 - 0.4 pb, substantially smaller than that in the non-relativisticlimit (0.4 - 1.6 pb). We also find a strong infrared sensitivity whichmanifests itself in a rather strong dependence on the mass for the $t$-channelgluons. The elementary cross section is then used in the Equivalent PhotonApproximation (EPA) in the impact parameter space to calculate the crosssection for $^{208}Pb+^{208}Pb \to ^{208}Pb + J/\psi J/\psi + ^{208}Pb$reaction. Distributions in rapidity of the $J/\psi J/\psi$ pair and invariantmass of the pair are shown.

european physical journal. c, particles and fields

The $\gamma \gamma \to J/\psi J/\psi$ reaction and the $J/\psi J/\psi$  pair production in exclusive ultraperipheral ultrarelativistic heavy ion  collisions